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A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: i. Head, ii. Head, iii. Head, iv. Head. The probability of obtaining a 'Tail' when the coin is tossed again is

Correct Answer: $$\frac{1}{2}$$

A coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed. If 8 possible outcomes are equally likely. Find the probability that the die shows a number greater than 4, if it is known that the first throw of the coin results in a tail

Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$

For each element in a set of size 2n, an unbiased coin is tossed. All the 2n coin tossed are independent. An element is chosen if the corresponding coin toss were head. The probability that exactly n elements are chosen is

$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$            is equal to = ?

An aircraft with wing aft tail configuration has tail efficiency of 0.95 and tail volume ratio of horizontal tail is 0.7. Determine pitching moment coefficient slope for the tail. Given lift curve slope of tail is 4.2 per rad. Consider downwash derivative as 0.6.

An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss ?

When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

Which of the following statements are true?
1. The classical approach to probability theory requires that the total number of possible outcomes be known or calculated and that each of the outcomes be equally likely.
2. A marginal probability is also known as unconditional probability.
3. For three independent events, the joint probability of the three events, P (ABC) = P (A) × P (B/A) × P (C/AB)
4. Two events are mutually exclusive, exhaustive and equally likely, the probability of either event A or B or both occurring P(A or B) = P(A) + P(B)

The probability is 1/2 that a coin will turn up heads on any toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?