 Hello friends and how are you all doing today? The question sees find the probability distribution of The number of doublets in three throws of a pair of dice Now let us solve this together Let X denote The number of doublets now the possible doublets known to us are one comma one two comma two three comma three four comma four five comma five and Six comma six when a pair of dice is thrown now clearly X can take the values of Zero one two and three right So probability of getting a doublet Will be equal to six out of 36 times That is equal to one by six so clearly probability of getting sorry probability of Not getting a doublet Will be equal to one minus probability of getting a doublet that is equal to five five six Now let us find out first of all probability when X is equal to zero That is probability of getting no doublet that is equal to Five by six into five by six into five by six as the pair of dice is thrown three times So after simplifying we have the value as one twenty five upon two one six Similarly, we will be finding out probability when X is equal to one that is probability of getting one doublet and two non-doublet that is equal to one by six into five by six into five by six or Five by six into one by six into five by six Or we can have five by six into five by six into one by six That is getting a doublet a non-doublet a non-doublet or a non-doublet first then a doublet and then a non-doublet or Non-doublet non-doublet or and then we get one doublet Then after simplifying it we have the value as three times One by six into five by six into five by six That is further equal to twenty five upon seventy two Now we need to find our probability of two doublet and one non-doublet that is one by six into one by six into five by six or five by six into one by six into one by six or We can have one by six into five by six into one by six That is three times the value one by six into one by six into five by six That we have as five by seventy two Lastly we need to find out probability when x is equal to three that is probability of all doublets That is equal to One by six into one by six into one by six that is one by two one six therefore Hence or therefore the required probability distribution is when the value of x was zero The probability is one twenty five upon two one six and the probability Sorry when x values one the probability is twenty five by seventy two Two then it's five upon seventy two and when the value of x is three then the probability is one upon two one six So this is the required answer to the given question. Hope you understood whole concept Well, do take care of your calculations and have a very nice day ahead