On a TV show a contestant is required to throw a die She the

On a TV show, a contestant is required to throw a die. She then tosses as many coins as there were spots shown on the die. If she throws exactly four heads, she wins $10,000. What is the probability she wins?

Solution

P(4 on die and 4 heads) = (1/6)*(1/2)^4 = 1/96

P(5 on die and 5 tosses out of which 4 are heads) = (1/6)*5C4 / 2^5 = 5/192

P(6 on die and 6 tosses out of which exactly 4 are heads) = (1/6)*(6C4)/2^6 = 5/128

Total probability = 1/96 + 5/192 + 5/128 = 29/384 ---> ANSWER