An unbiased coin is tossed 8 times. The proba | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The total number of outcomes when a coin is tossed $8$ times is $2^8 = 256$.Let $H$ denote head and $T$ denote tail.We want the number of outcomes

Vedclass · Accepted Answer

$\frac{5}{128}$

Vedclass · Answer

(B) The total number of outcomes when a coin is tossed $8$ times is $2^8 = 256$.Let $H$ denote head and $T$ denote tail.We want the number of outcomes where $H$ appears consecutively at least $5$ times.Case $1$: Exactly $5$ consecutive heads.- $HHHHHTTT$ (and shifts: $THHHHHT T, TTHHHHHT, TTTHHHHH$): $4$ ways.- $HHHHHTHT$ (and shifts: $THHHHHTH, TTHHHHHT$): $3$ ways.- $HHHHHTTH$ (and shifts: $THHHHHTT, TTHHHHHT$): $3$ ways.- $THHHHHTH$ is already counted.- $HHHHHTHH$ is not possible as it would be $6$ heads.Using the inclusion-exclusion principle or manual counting for sequences of length $8$ with at least $5$ consecutive $H$:- Sequences with $5$ consecutive $H$: $HHHHHTXX$ ($4$ ways),$THHHHHTX$ ($3$ ways),$XXTHHHHH$ ($4$ ways).- Total favorable outcomes are $10$.Probability $= \frac{10}{256} = \frac{5}{128}$.

An unbiased coin is tossed $8$ times. The probability that head appears consecutively at least $5$ times is

Similar Questions

The probability that an event will fail to happen is $0.05$. The probability that the event will take place on $4$ consecutive occasions is

The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least $0.96$ is:

If $X$ is a binomial variable with range $\{0, 1, 2, 3, 4\}$ and $P(X=3) = 3P(X=4)$,then the parameter $p$ of the binomial distribution is:

The probability of a man hitting a target is $3/4$. He tries $5$ times. What is the probability that he hits the target at least $3$ times?

In a family with $4$ children, the probability that there are at least two girls is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module