Question

The probability that Jess will answer any question correctly, independently of her answer to any other

question, is p (p > 0). Let the random variable Y be the number of questions that Jess answers
correctly in any set of 25.

If Pr(Y > 23) = 6 x Pr(Y = 25), show that the value of p is 5/6

Answer 1

I hope my answer helps :)

Explanation:

P(Y > 23) = P(Y = 24) + P(Y = 25)

6P(Y=25) = P(Y = 24) + P(Y = 25)

6 = P(Y = 24)/P(Y = 25)+ 1

5 = (²⁵C24×p²⁴×q¹)/(²⁵C25×p²⁵×q⁰)

Since you know that q = 1 - p,

5 = 25{[p²⁴(1 - p)]/p²⁵}

1/5 = (p²⁴ - p²⁵)/p²⁵

1/5 = p^(-1) - 1

6/5 = 1/p

p = 5/6 (shown)