Question

3. Determine the following probabilities: (a) Probability you get at least one 3 in four throws of a single die. Assume the dice is fair. (b) Probability that you get at least one "double 3" in 24 rolls of a pair of dice. A double 3 is when both dice are 3. (c) You toss two dice. Find the probability that at least one dice is a 4. (d) Find the probability of drawing 2 hearts in succession from a deck of cards

Answer 1

"(a) No. of trials = 4 rightarrow Throwing die P(r greaterthanorequalto 1) = Probability of getting 3 at least one time r = getting 3 in throw die p = probability of getting 3 in 1 throw = 1/6 q = Probability of not getting 3 = 5/6 Here we can apply binomial probability distribution P(r greaterthanorequalto 1) = P(r = 1) + P(r = 2) + P(r = 3) + P(r = 4) or we may write P(r greaterthanorequalto 1) = 1 - P(r = 0) P(r) = n_c_r p^r q^n - r = 4_c_0 (1/6)^0 (5/6)^4 - 0 = (5/6)^4 P(r greaterthanorequalto 1) = 1 - (5/6)^4 P(r greaterthanorequalto 1) = 1 - 0.4822 P(r greaterthanorequalto 1) = 0.5178 n = 24 rightarrow Throwing 2 die r rightarrow double 3 p = probability of getting ""double 3"" = 1/36 q = probability of getting other then double = 35/36 P(r greaterthanorequalto 1) = 1 - P(r = 0) P(r greaterthanorequalto 1) = 1 - n_c_0 p^r q^n - r"