Answer to Question #315969 in Statistics and Probability for Fish

Question

if two coins and a dice are thrown at once, what is the probability of getting two heads and six or one tail, one head and a three?

Answer 1

Assuming coins are fair, the probability of getting heads on a coin is equal to the probability of getting tails, p_head=p_tail=1/2. Similarly, assuming a dice is fair, the probability of getting any number on a dice is equal, p_x=1/6.

Probabilities of independent events that happen simultaneously should be multiplied. Hence, the probability of getting two heads and six on a dice equals

p_head*p_head*p₆=1/2*1/2*1/6=1/24.

Probabilities of disjoint events that both can happen should be added. Hence, the probability of getting one head and one tail and a three is

(p_head*p_tail+p_tail*p_head)*p₃=(1/2*1/2+1/2*1/2)*1/6=1/12.

Then the total probability is

1/24+1/12=3/24.

ANSWER: 3/24