Answer:
P(X < 3) = 0.9375
Step-by-step explanation:
If the coins tossed by the 3 people all turn up the same, it means that we will have either; HHH or TTT
H is head and T is tail.
Thus; the probability of failure in each trial is;
q = P(HHH) + P(TTT)
P(H) = ½ and P(T) = ½.
Hence;
q = P(HHH) + P(TTT) = (½ × ½ × ½) + (½ × ½ × ½) = ⅛ + ⅛ = ¼ = 0.25
In binomial probability, p = 1 - q
Thus; p = 1 - 0.25 = 0.75
Now to find the probability that fewer than 3 tosses are needed is given by the expression;
P(X < 3) = P(1) + P(2)
Now, because the toss trials are independent, it means that x = 1.
Since x = 1,we can make use of geometric distribution formula which is given by;
P(X = x) = p^(x) • q^(n - x)
Thus;
P(1) = 0.75^(1) × 0.25^(1 - 1)
P(1) = 0.75 × 1
P(1) = 0.75
P(2) = 0.75^(1) × 0.25^(2 - 1)
P(2) = 0.75 × 0.25
P(2) = 0. 75 × 0.25
P(2) = 0.1875
Thus;
P(X < 3) = 0.75 + 0.1875
P(X < 3) = 0.9375
