Solve left(.95right)^48left(1-.95right)^2=0.2648!2!/50!

$${ \left(.95 \right) }^{ 48 } { \left(1-.95 \right) }^{ 2 } =0.26 \frac{ 48 ! 2 ! }{ 50 ! }$$

Verify

Solution Steps

Calculate 0.95 to the power of 48 and get 0.085257590334308398087860807862421154731500384756109847579645023785133162164129316806793212890625.

$$0.085257590334308398087860807862421154731500384756109847579645023785133162164129316806793212890625\left(1-0.95\right)^{2}=0.26\times \frac{48!\times 2!}{50!}$$

Subtract 0.95 from 1 to get 0.05.

$$0.085257590334308398087860807862421154731500384756109847579645023785133162164129316806793212890625\times 0.05^{2}=0.26\times \frac{48!\times 2!}{50!}$$

Calculate 0.05 to the power of 2 and get 0.0025.

$$0.085257590334308398087860807862421154731500384756109847579645023785133162164129316806793212890625\times 0.0025=0.26\times \frac{48!\times 2!}{50!}$$

Multiply 0.085257590334308398087860807862421154731500384756109847579645023785133162164129316806793212890625 and 0.0025 to get 0.0002131439758357709952196520196560528868287509618902746189491125594628329054103232920169830322265625.

$$0.0002131439758357709952196520196560528868287509618902746189491125594628329054103232920169830322265625=0.26\times \frac{48!\times 2!}{50!}$$

The factorial of 48 is 12413915592536072670862289047373375038521486354677760000000000.

$$0.0002131439758357709952196520196560528868287509618902746189491125594628329054103232920169830322265625=0.26\times \frac{12413915592536072670862289047373375038521486354677760000000000\times 2!}{50!}$$

The factorial of 2 is 2.

$$0.0002131439758357709952196520196560528868287509618902746189491125594628329054103232920169830322265625=0.26\times \frac{12413915592536072670862289047373375038521486354677760000000000\times 2}{50!}$$

Multiply 12413915592536072670862289047373375038521486354677760000000000 and 2 to get 24827831185072145341724578094746750077042972709355520000000000.

$$0.0002131439758357709952196520196560528868287509618902746189491125594628329054103232920169830322265625=0.26\times \frac{24827831185072145341724578094746750077042972709355520000000000}{50!}$$

The factorial of 50 is 30414093201713378043612608166064768844377641568960512000000000000.

$$0.0002131439758357709952196520196560528868287509618902746189491125594628329054103232920169830322265625=0.26\times \frac{24827831185072145341724578094746750077042972709355520000000000}{30414093201713378043612608166064768844377641568960512000000000000}$$

Reduce the fraction \frac{24827831185072145341724578094746750077042972709355520000000000}{30414093201713378043612608166064768844377641568960512000000000000} to lowest terms by extracting and canceling out 24827831185072145341724578094746750077042972709355520000000000.

$$0.0002131439758357709952196520196560528868287509618902746189491125594628329054103232920169830322265625=0.26\times \frac{1}{1225}$$

Multiply 0.26 and \frac{1}{1225} to get \frac{13}{61250}.

$$0.0002131439758357709952196520196560528868287509618902746189491125594628329054103232920169830322265625=\frac{13}{61250}$$

Convert decimal number 0.0002131439758357709952196520196560528868287509618902746189491125594628329054103232920169830322265625 to fraction \frac{23997878253756106444997335735942416102218125380085922630082241}{10000000000}. Reduce the fraction \frac{23997878253756106444997335735942416102218125380085922630082241}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{23997878253756106444997335735942416102218125380085922630082241}{112589990684262400000000000000000000000000000000000000000000000000}=\frac{13}{61250}$$

Least common multiple of 112589990684262400000000000000000000000000000000000000000000000000 and 61250 is 5516909543528857600000000000000000000000000000000000000000000000000. Convert \frac{23997878253756106444997335735942416102218125380085922630082241}{112589990684262400000000000000000000000000000000000000000000000000} and \frac{13}{61250} to fractions with denominator 5516909543528857600000000000000000000000000000000000000000000000000.

$$\frac{1175896034434049215804869451061178389008688143624210208874029809}{5516909543528857600000000000000000000000000000000000000000000000000}=\frac{1170935903116328960000000000000000000000000000000000000000000000}{5516909543528857600000000000000000000000000000000000000000000000000}$$

Compare \frac{1175896034434049215804869451061178389008688143624210208874029809}{5516909543528857600000000000000000000000000000000000000000000000000} and \frac{1170935903116328960000000000000000000000000000000000000000000000}{5516909543528857600000000000000000000000000000000000000000000000000}.

$$\text{false}$$