Probability Quiz Set 020

Total number of marbles is 17. Combinations of 2 marbles that are possible = ¹⁷C₂ = ${17 × 16}/2$ = 136. If one of the two balls is orange, then both balls will be orange in ⁸C₂ = ${8 × (8 - 1)}/2$ = 28 ways. The number of ways in which non-orange can be drawn out are 8 × (6 + 3). So total favorable outcomes = 28 + 8 × 9 = 100, and the probability is 100/136 = ${25/34}$.

There are 12 such cards in the entire deck of 52 cards, so the required probability is 12/52 = 3/13.

P(E) + P(non-occurrence of E) is always = 1. So P(non-occurrence of E) = 1 - P(E) = 0.46.

Total outcomes = 36. Favorable are 2, which are: (1, 1), (1, 1). Probability = 2/36 = 1/18.

One of the two is going to win. Probability of A's defeat is 1 - 0.2 = 0.8, which is the probability of B's victory.