1. The probability of drawing 2 marbles of different colors from a bag has to be determined given that the bag contains 3 green, 4 yellow and and five red marbles.

There are 3+4+5 = 12 marbles in the bag. The number of ways of picking 2 marbles from the...

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1. The probability of drawing 2 marbles of different colors from a bag has to be determined given that the bag contains 3 green, 4 yellow and and five red marbles.

There are 3+4+5 = 12 marbles in the bag. The number of ways of picking 2 marbles from the bag is 12*11 = 132. The number of ways of picking 2 marbles that are the same color is 3*2 + 4*3 + 5*4 = 6 + 12 + 20 = 38. This gives the number of ways of picking 2 marbles with a different color as 132 - 38 = 94

The probability of picking two marbles with a different color is 94/132

2. When a coin is tossed there is an equal probability of getting either heads or tails and this is equal to 0.5. When a coin is tossed 4 times, the probability of getting at least 2 heads is the 1 - (probability of getting 0 heads + probability of getting 1 head) = 1 - ((1/2)^4 + (1/2)^4*4) = 1 - 5/16 = 11/16.