Probability

Numbers divisible by 7 between 1 and 100 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98. There are 14 such numbers. The probability is 14/100, which simplifies to 7/50.

Total tosses = 75. Heads = 25. Tails = 75 - 25 = 50. Probability of tail = 50/75 = 2/3.

Total bulbs = 7 + 20 = 27. Number of undefective bulbs = 20. Probability = 20 / 27.

Sample space for two tosses is {HH, HT, TH, TT}. Only one outcome is TT. Probability is 1/4.

The total number of balls is 2 + 3 + 5 = 10. The probability of drawing a red ball is the number of red balls divided by the total number of balls, which is 2/10.

Two coins tossed result in HH, HT, TH, or TT. Exactly one tail corresponds to HT or TH. The total outcomes are 600. The number of times one head occurred is 192, which implies the other coin was a tail. Thus, the probability is 192/600.

Total tosses = 600. Two heads = 138, one head = 192, no heads (two tails) = 270. Probability of two tails = 270 / 600 = 27/60 = 9/20.

Total outcomes for 4 tosses = 2^4 = 16. The only case with no heads is TTTT (1 outcome). Probability of at least one head = 1 - P(no heads) = 1 - 1/16 = 15/16.

There are 2 red queens (heart and diamond) in a deck of 52 cards. Probability = 2/52 = 1/26.

There are 2 black kings (King of Spades and King of Clubs) in a deck of 52 cards. Probability = 2/52 = 1/26.

There are 4 queens and 4 jacks in a deck of 52 cards. Total favorable outcomes = 4 + 4 = 8. Probability = 8/52 = 2/13.

There are 4 queens in a deck of 52 cards. The probability of drawing a queen is 4/52 = 1/13. The probability of not drawing a queen is 1 - 1/13 = 12/13.

There are 4 kings and 4 jacks in a 52-card deck, totaling 8 favorable outcomes. The probability is 8/52, which simplifies to 2/13.