A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is p , then 96p is equal to _____.

Step-by-step solution

Let the outcomes of the 8 tosses be denoted by X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈ . Let A be the number of heads in the first 3 tosses ( X₁, X₂, X₃ ). Let B be the number of heads in the next 3 tosses ( X₄, X₅, X₆ ). Let C be the number of heads in the last 2 tosses ( X₇, X₈ ). According to the given conditions: Number of heads in the first six tosses: A + B = 4 Number of heads in the last five tosses: B + C = 3 Since C is the number of heads in 2 tosses, C 2 . Thus, B = 3 - C 1 . Also, B 3 . The possible values for B