(i) Primes 7 and 11 give 8 pairs, P = 8/36 = 2/9. (ii) P(different) = 1 – P(same) = 1 – 13/36 = 23/36. (iii) Favourable outcomes {HHT, HTH}, P = 2/8 = 1/4. (iv) Last digit 2 or 4, P = ...
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(i) The sample space is S = {(Samosa, Chai), (Samosa, Lassi), (Pakora, Chai), (Pakora, Lassi), (Bhaji, Chai), (Bhaji, Lassi)}, giving 6 outcomes. (ii) The event selecting Samosa is E = {(Samosa, Chai), (Samosa, Lassi)}.
When rolling a 6-sided die, sample space is {1, 2, 3, 4, 5, 6}, giving 6 possible outcomes. The even numbers are 2, 4, and 6, so probability is 3/6 = 1/2 = 0.5.
In an illustrative 20-toss trial getting 11 heads and 9 tails, experimental probability of heads is 11 / 20 = 0.55. For the next toss, because a coin has no memory, tails probability remains 1 / 2 = 0.5.
The probability for Arts Club is 11 / 40 = 0.275 (27.5%). The sample proportion for Sports Club is 9 / 40. Across 800 students, the estimated count is (9 / 40) x 800 = 180 students.