Probability is also known as the math of chance. This means the possibility, that deals in the occurrence of a likely affair. The value is deputed from zero to one. In math, Probability has been manifest to estimate how likely affairs are to occur. Basically, probability is the extent to which something is to be expected to occur. Probability To understand probability more accurately, let us understand an example of rolling a dice, the possible outcomes are – 1, 2, 3, 4, 5, and 6. The probability of happening any of the likely affairs is 1/6. As the possibility of happening any of the affairs is the same so there is an equal possibility of happening any favorable affair, in this case, it is either of two 1/6 or 50/3. Formula of Probability
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Similar QuestionsQuestion 1: If four coins are tossed, what is the probability of occurring neither 4 heads nor 4 tails? Solution:
Question 2: If four coins are tossed, find the possibility that there should be two heads and two tails. Solution:
Question 3: If you toss a coin 4 times, what is the probability of getting all heads? Solution:
There are $6$ remaining games. The desired criteria is that Heat wins at least $4$, when given that Heat lost the first 1. This is a binomial distribution; so named because of the use of the binomial coefficient to count number of permutations of outcomes that match the desired criteria. The probability of exactly $k$ successes in $n$ trials with probability $p$ of success in any trial, is: $${n\choose k}p^k(1-p)^{n-k} \;=\; \,^n\mathrm{\large C}_k\;p^k(1-p)^{n-k} \;=\; \frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}$$ So: $\mathbb{\large P}(\text{win at least }4\text{ more of }6) = {6\choose 4}\left(\frac 12\right)^4\left(\frac 12\right)^2+{6\choose 5}\left(\frac 12\right)^5\left(\frac 12\right)^1+{6\choose 6}\left(\frac 12\right)^6\left(\frac 12\right)^0$. $$\therefore \mathbb{\large P}(\text{win at least }5\text{ more of }6) = \frac 1{2^6}\left(\frac{6!}{4!2!}+\frac{6!}{5!1!}+\frac{6!}{6!0!}\right)$$
Option 1 : \(\dfrac{15}{64}\)
15 Questions 45 Marks 15 Mins
Given: 6 unbiased coins are tossed Concept Used: Probability = Number of desire event / Number of total event Calculation: Total number of events = 26 = 64 Exactly 4 tail can be happen in 6C4 ways = \(6! \over {4! \times (6 - 4)!}\) = 15 ∴ The probability of getting exactly 4 tails when 6 unbiased coins are tossed is 15/64. India’s #1 Learning Platform Start Complete Exam Preparation
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