Probability

A standard deck has 52 cards, of which 26 are red (hearts and diamonds). The probability of drawing a red card is 26/52, which simplifies to 1/2.

Outcomes: {1, 2, 3, 4, 5, 6}. Odd numbers: {1, 3, 5}. Less than 5: {1, 2, 3, 4}. Union of sets: {1, 2, 3, 4, 5}. Probability = 5/6.

There are two scenarios: (Red from Bag 1 AND Green from Bag 2) OR (Green from Bag 1 AND Red from Bag 2). Probabilities are (5/8 * 6/10) + (3/8 * 4/10) = 30/80 + 12/80 = 42/80 = 21/40.

Total outcomes for two dice = 36. Favorable outcomes for sum 5: (1,4), (2,3), (3,2), (4,1). There are 4 outcomes. Probability = 4/36 = 1/9.

Total balls = 10 + 7 = 17. Probability of red = 10/17. Probability of not red = 1 - 10/17 = 7/17.

Total balls = 12 + 10 = 22. Probability of red = 12 / 22 = 6 / 11.

Numbers containing a 0 between 1 and 100 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. There are 10 such numbers. The probability is 10/100.

Total ways to choose 2 animals from 5 is 5C2 = 10. Ways to choose 2 doves is 3C2 = 3. Ways to choose 2 rabbits is 2C2 = 1. Total matched pairs = 3 + 1 = 4. Probability = 4/10 = 40%.

Total students = 60, boys = 35, so girls = 60 - 35 = 25. Probability of picking a girl is 25/60 = 5/12.

Probability is defined as the number of favorable outcomes divided by the total number of outcomes. Here, there are x orange candies out of 16 total candies.

Total outcomes = 36. Outcomes with one odd and one even: (O,E) or (E,O). There are 3 odd (1,3,5) and 3 even (2,4,6) numbers. (O,E) has 3*3=9 outcomes. (E,O) has 3*3=9 outcomes. Total favorable = 18. Probability = 18/36 = 1/2.

The total number of tosses is 100. The frequency of heads is 25. The probability is 25/100, which simplifies to 1/4.

The probability of an event is the number of favorable outcomes divided by the total number of trials. Since there are 100 tosses and 54 are heads, there are 100 - 54 = 46 tails. The probability of a tail is 46/100 = 0.46.

A standard die has six equally likely outcomes. Outcomes greater than 3 are 4, 5, and 6, so the probability is 3/6 = 1/2.

Total outcomes for two dice are 36. Outcomes with a product as a multiple of 4 are: (1,4), (2,2), (2,4), (2,6), (3,4), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (6,2), (6,4), (6,6). Counting these gives 15 favorable outcomes, so the probability is 15/36 = 5/12.