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Marcus buys scratch cards one by one until he finds a winning card. The probability that a card is a winner is \(0.15\). We assume the draws are independent. Let \(X\) be the random variable representing the rank of his first winning card.
State the distribution followed by \(X\).
Represent the situation with a tree diagram for the first three trials and use it to find \(P(X=2)\).
Calculate \(P(X=5)\) and interpret the result.
Calculate \(P(X \leq 3)\) and interpret the result.
Calculate \(E(X)\) and interpret the result.
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