Question

I toss 3 coind and roll 2 dice.what is the probability of all the coins landing on talks rolling a 10. It is not important whether 1 or both events happen

Answer 1

Answer: 19/96

Work Shown

Define the two events

• A = all 3 coins land tails
• B = the two dice sum to 10

Then,

• P(A) = (1/2)*(1/2)*(1/2) = 1/8
• P(B) = 3/36 = 1/12

Note: There are 3 ways to sum to 10 (which are 4+6, 5+5, and 6+4) out of 6*6 = 36 ways to roll two dice.

Furthermore,

P(A and B) = P(A)*P(B) ... independent events

P(A and B) = (1/8)*(1/12)

P(A and B) = 1/96

And finally,

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 1/8 + 1/12 - 1/96

P(A or B) = 12/96 + 8/96 - 1/96

P(A or B) = 19/96 is the probability of either event A or event B (or both) happening