Question

An unbiased coin is tossed 15 times. In how many ways can the coin land tails either exactly 8 times orexactly 5 times?

Answer 1

Answer:

Probability to get tails exactly 8 times or exactly 5 times is 0.29

Step-by-step explanation:

No of ways the coins lands tails exactly 8 times

P(8) = 15C8 × $0.5^{8}$ × $0.5^{15-8}$

No of ways the coin lands tails exactly 5 times

P(5) = 15C5 × $0.5^{5}$ × $0.5^{15-5}$

Probability to get tails exactly 8 times or 5 times

P(8)+P(5) =  15C8 × $0.5^{15}$ + 15C5 × $0.5^{15}$

P = $0.5^{15}$ (  15C8 + 15C5 )

P = $0.5^{15}$ ( (  $\frac{15!}{8!(15-8)!}$  ) + ( $\frac{15!}{5!(15-5)!}$ ) )

P = $0.5^{15}$ ( 6435 + 3003 )

P = $0.5^{15}$ ( 9438)

P = $0.5^{14}$ ( 4719)

P =  $\frac{4719}{16384}$

P = 0.29