Tag: some more terms in probability

Questions Related to some more terms in probability

For the special rule of multiplication of probability, the events must be

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. Empirical

  2. Bayesian

  3. Independent

  4. none of these

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Correct Option: C

In a simultaneous throw of two dice, what is the probability of getting a total of 10 or 11 ?

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $\displaystyle \frac{7}{12}$

  2. $\displaystyle \frac{5}{36}$

  3. $\displaystyle \frac{1}{6}$

  4. $\displaystyle \frac{1}{4}$

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Correct Option: B
Explanation:
Let A denotes the event of getting a total of 10 and B denotes the event of getting a total of 11.
Total outcomes = $6\times 6 $
A= {(5,5),(6,4),(4,6)}
n(A) = $3$
$\therefore $ p(A) = $\dfrac {3}{36}  $
B={(6,5),(5,6)}
n(B) = 2
$\therefore $ p(B)= $\dfrac {2}{36}  $
$\therefore $ p(A or B) = p(A) + p(B) 
                   = $\dfrac {3}{36} + \dfrac {2}{36} $
                   = $\dfrac {5}{36} $
Option B is correct.

How many times must a man toss a fair coin, so that the probability of having at least one head is more than $80 \%?$

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $3$

  2. $>3$

  3. $<3$

  4. none of these

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Correct Option: B
Explanation:
In any fair coin toss, P (getting a head) = P (getting a tail) i.e., p=q=$\dfrac 12$
We need to find n such that the probability of getting at least one head is more than $80\%$
$P(X≥1)=1−P(X<1)>80\%$
$\implies 1−P(X=0)>\dfrac 8{10}\\\implies P(X=0)<1−\dfrac 8{10}\\\implies P(X=0)<\dfrac 2{10} or P(X=0)<\dfrac 15$
For a bionomial distribution, $P(X=0)=^nC _0\left(\dfrac 12\right)^0\left(\dfrac 12\right)^{n−0}=\left(\dfrac 12\right)^n$
$\implies \left(\dfrac 12\right)^n<\dfrac 1{5}\\\implies 2^n>5$
Since $2^1=2,2^2=4, 2^3=8,2^4=16$, the minimum value for n that satisfies the inequality is $n=3$, i.e, the coin should be tossed $3$ or more times.

Calculate the probability that a spinner, having the numbers one through five evenly spaced, will land on an odd number exactly once if the spinner is used three times.

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $\dfrac {12}{125}$

  2. $\dfrac {18}{125}$

  3. $\dfrac {27}{125}$

  4. $\dfrac {36}{125}$

  5. $\dfrac {54}{125}$

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Correct Option: D
Explanation:

Total possible combinations when spinner used three times is $5 \times 5 \times 5 = 125$.
Out of three times, inexactly one number is odd implies the other two numbers are even.
The possible combinations such that exactly one number is odd is $3 \times 2 \times 2 + 2 \times 3 \times 2 + 2 \times 2 \times 3 = 36$.
The probability is $\dfrac {36}{125}$.

A bag contains $10$ balls, each labelled with a different integer from $1$ to $10$, inclusive. If $2$ balls are drawn simultaneously from the bag at random, calculate the probability that the sum of the integers on the balls drawn will be greater than $6$.

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $0.41$

  2. $0.43$

  3. $0.60$

  4. $0.76$

  5. $0.87$

Show answer
Correct Option: E
Explanation:

Out of $10$ balls , $2$ balls can be selected in ${ ^{ 10 }{ C } } _{ 2 } = 45$
Number of ways of selecting $2$ balls such that sum is less than or equal to $6$ is $6$
Probability that the sum of integers on the balls drawn will be greater than $6$ is $1-\dfrac {6}{45} = \dfrac {39}{45} = 0.87$